Question

the sum of the first 3 terms of any a.p is 12 and the sum of the next 5 terms is 24 the what is the common difference?

Answer 1

Answer:

sum

Step-by-step explanation:

because sum is doing in both cases.

Answer 2

Answer:

d = 1/5

Step-by-step explanation:

$\frac{n}{2} (2a + (n - 1)d)$

where a is the starting value, n is the number of terms from starting, and d is the common difference.

$for \: {1}^{st} condition \: \frac{3}{2} (2a + (3 - 1)d) = 12 \\ 2a + 2d = \frac{12 \times 2}{3} \\ 2(a + d) = \frac{24}{3} = 8 \\ a + d = 4 - - - - (1)$

for second situation, sum of the next 5 terms is 24, which means sun of first 8 terms is 12 + 24 which is equal to 36.

$\frac{8}{2} (2a + (8 - 1)d) = 36 \\ 4(2a + 7d) = 36 \\ 2a + 7d = 9 - - - - (2)$

$subtract \:2 \times (1 )\: from \: (2) \\ \\ 2a + 7d = 9 \\ - (2a + 2d = 8) \\ - - - - - - - - - \\ 5d = 1 \\ d = \frac{1}{5}$